Numerical Study of Rayleigh-Benard Problem under the Effect of Magnetic Field
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Abstract
In this paper, a linear stability analysis is studied for Rayliegh-Benard problem with the effect of magnetic field, a perturbation equations is solved numerically by using spectral Chebyshev tau method, the boundaries are considered both are free, both are rigid, the lower is free and the upper is rigid, the results were illustrated graphically and compared with previous studies.
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References
- S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, Oxford University Press, Oxford, 1961.
- S. Chandrasekhar, The instability of a layer of fluid heated below and subject to Coriolis forces, Proc. R. Soc. Lond. A. 217 (1953), 306-327.
- S. Chandrasekhar, The instability of a layer of fluid heated below and subject to the simultaneous action of a magnetic field and rotation, Proc. R. Soc. Lond. A. 225 (1954), 173-184.
- S. Chandrasekhar, D.D. Elbert, The instability of a layer of fluid heated below and subject to Coriolis forces. II, Proc. R. Soc. Lond. A. 231 (1955), 198-210.
- A.J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967), 12-26.
- J.J. Dongarra, B. Straughan, D.W. Walker, Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems, Appl. Numer. Math. 22 (1996), 399-434.
- L. Fox, Chebyshev Methods for Ordinary Differential Equations, Computer J. 4 (1962), 318-331.
- M.A. Hernandez, Chebyshev's approximation algorithms and applications, Comput. Math. Appl. 41 (2001), 433-445.
- A.A. Hill, Convection in porous media and Legendre, Chebyshev Galerkin methods, Ph.D. Thesis, Durham University, 2005.
- D. Johnson, Chebyshev Polynomials in the Spectral Tau Method and Applications to Eigenvalue Problems, NASA Contractor Report 198451, 1996.
- S. Talukdar, A study of some steady and unsteady MHD flow problems with heat and mass transfer, Ph.D. Thesis, Gauhati University, 2013.
- D.Y. Tzou, Instability of Nanofluids in Natural Convection, J. Heat Transfer, 130 (2008), 072401.
- B.-F. Wang, D.-J. Ma, Z.-W. Guo, D.-J. Sun, Linear instability analysis of Rayleigh-B ´enard convection in a cylinder with traveling magnetic field, J. Crystal Growth, 400 (2014), 49-53.
- D. Yadav, J. Wang, R. Bhargava, J. Lee, H.H. Cho, Numerical investigation of the effect of magnetic field on the onset of nanofluid convection, Appl. Therm. Eng. 103 (2016), 1441-1449.